4x(1-x)=1

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Solution for 4x(1-x)=1 equation:


Simplifying
4x(1 + -1x) = 1
(1 * 4x + -1x * 4x) = 1
(4x + -4x2) = 1

Solving
4x + -4x2 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + 4x + -4x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 4x + -4x2 = 0

Factor a trinomial.
(-1 + 2x)(1 + -2x) = 0

Subproblem 1

Set the factor '(-1 + 2x)' equal to zero and attempt to solve: Simplifying -1 + 2x = 0 Solving -1 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2x = 0 + 1 2x = 0 + 1 Combine like terms: 0 + 1 = 1 2x = 1 Divide each side by '2'. x = 0.5 Simplifying x = 0.5

Subproblem 2

Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5

Solution

x = {0.5, 0.5}

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